# Using Above Below Primitive to Test Whether Two Lines Intersect in Java

• Last Updated : 05 Nov, 2021

Above Below Primitive is the method to check whether the lines are intersecting or not by comparing their endpoints. Here is a JAVA program which uses above below primitive to test whether two lines intersect with each other or not. This approach only returns true if one endpoint of the line is on the left of the other line’s left endpoint and its right endpoint is on the right of other line’s endpoint.

Example

```Input:
End Points of first line
x1 = 2, y1 = 3
x2 = 6, y2 = 4
End Points of second line
p1 = 3, q1 = 4
p2 = 7, q2 = 1
Output:
Equation 1: (1)x+(-4)y+(10) = 0
Equation 2: (-3)x+(-4)y+(25) = 0
Intersecting```

Approach

```Find the segment first line as a1.
if a1 < 0
Find the segment of line 2 as a2
if a2 >= 0
print intersecting
otherwise
print not intersecting.
else if a1 >0
Find the segment of line 2 as a2
if a2 <= 0
print intersecting.
otherwise
print not intersecting.```

Below is the implementation of the above approach.

## Java

 `// This is a java program to find whether two lines``// intersect or not using above and below primitive``public` `class` `Main {``    ``public` `static` `void` `check(``int` `x1, ``int` `x2, ``int` `y1, ``int` `y2,``                             ``int` `p1, ``int` `p2, ``int` `q1, ``int` `q2)``    ``{ ``// Segment of line 1 is stored as a1` `        ``int` `a1 = (y2 - y1) * p1 + (x1 - x2) * q1``                 ``+ (x2 * y1 - x1 * y2);` `        ``if` `(a1 < ``0``) {``            ``// Segment of line 2 is stored as a2``            ``int` `a2 = (y2 - y1) * p2 + (x1 - x2) * q2``                     ``+ (x2 * y1 - x1 * y2);` `            ``if` `(a2 >= ``0``)``                ``System.out.println(``"Intersecting"``);` `            ``else` `if` `(a2 < ``0``)``                ``System.out.println(``"Not intersecting"``);``        ``}` `        ``else` `if` `(a1 > ``0``) {` `            ``int` `a2 = (y2 - y1) * p2 + (x1 - x2) * q2``                     ``+ (x2 * y1 - x1 * y2);` `            ``if` `(a2 <= ``0``)``                ``System.out.println(``"Intersecting"``);` `            ``else` `if` `(a2 > ``0``)``                ``System.out.println(``"Not intersecting"``);``        ``}` `        ``// lines are coincinding``        ``else``            ``System.out.println(``                ``"points are lying on the line"``);``    ``}``    ``// Driver Code``    ``public` `static` `void` `main(String args[])``    ``{``        ``// Taking the coordinates of first line as input``        ``int` `x1 = ``2``, y1 = ``3``;``        ``int` `x2 = ``6``, y2 = ``4``;` `        ``// Equation of line using slope point form``        ``System.out.println(``"Equation 1: ("` `+ (y2 - y1)``                           ``+ ``")x+("` `+ (x1 - x2) + ``")y+("``                           ``+ (x2 * y1 - x1 * y2) + ``") = 0"``);` `        ``// Taking the coordinates of second line as input``        ``int` `p1 = ``3``, q1 = ``4``;``        ``int` `p2 = ``7``, q2 = ``1``;` `        ``// Equation of line using slope point form``        ``System.out.println(``"Equation 2: ("` `+ (q2 - q1)``                           ``+ ``")x+("` `+ (p1 - p2) + ``")y+("``                           ``+ (p2 * q1 - p1 * q2) + ``") = 0"``);` `        ``check(x1, x2, y1, y2, p1, p2, q1, q2);``    ``}``}`

Output

```Equation 1: (1)x+(-4)y+(10) = 0
Equation 2: (-3)x+(-4)y+(25) = 0
Intersecting```

Time Complexity: O(1)

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